How do you find the mean, median, and mode of the following frequency distribution table?

Question

How do you find the mean, median, and mode of the following frequency distribution table?

Score* (Number of Students)
10 - 6
9 - 13
8 - 12
7 - 11
6 - 13
5 - 5

1 Answer

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Answer 1 · 2018-08-06T12:06:42

$Mean ¯ ¯ ¯ X = 67.55, Median M = 8 and Mode Z = 13$ $"Mean "bar(X)=67.55 ," Median " M=8 and "Mode "Z=13$

Explanation:

Let us ordering the data from least to greatest.

Please see the table given below.

Let ,

$x_{i} = Score and f_{i} = Number of students$ $x_i="Score" and f_i="Number of students"$

$N = Total Number of students$ $N="Total Number of students"$

$and C f_{i} = Comulative frequency$ $and Cf_i="Comulative frequency"$

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$(1) Mean ¯ ¯ ¯ X = \frac{\sum f_{i} x_{i}}{N} = \frac{453}{60} = 67.55$ $color(red)((1)"Mean " bar(X)=(sum f_ix_i)/N =(453)/60=67.55$

$Median M = (\frac{N + 1}{2}) t h score \to x_{i}$ $"Median " M=((N+1)/2)th " score"to x_i$

$Median M = (\frac{60 + 1}{2}) t h score \to x_{i}$ $"Median " M=((60+1)/2)th " score"tox_i$

$Median M = ((30.5) t h score \to x_{i}$ $"Median " M=((30.5)th " score"tox_i$

Now ,from $C f_{i} \to 29 < 30.5, and 30.5 > 41$ $Cf_ito29 < 30.5 , and 30.5 > 41$

So, see the cell in the green color :

$C f_{i} = 41 \to for x_{i} = 8$ $color(green)(Cf_i=41to "for "x_i=8$

$:."Median " M=8$

$(3)" Mode " Z="Frequency repeated in the set of data,"$
$color(white)((3)" Mode " Z=)"maximum number of times"$

$:.color(orange)(" Mode " Z=13to"see the yellow color in table for "f_i.$

$i.e." Mode " Z=13$

Hence ,

$"Mean "bar(X)=67.55 ," Median " M=8 and "Mode "Z=13$

Science

Math

Humanities

... and beyond

How do you find the mean, median, and mode of the following frequency distribution table?

Score* (Number of Students)
10 - 6
9 - 13
8 - 12
7 - 11
6 - 13
5 - 5

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

How do you find the mean, median, and mode of the following frequency distribution table?

Score* (Number of Students) 10 - 6 9 - 13 8 - 12 7 - 11 6 - 13 5 - 5

1 Answer

Explanation:

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Impact of this question

Score* (Number of Students)
10 - 6
9 - 13
8 - 12
7 - 11
6 - 13
5 - 5